1. Field of the Invention
The present invention relates generally to a filter architecture using a neural network, and to a method and an apparatus for implementing the architecture.
2. Description of the Related Art
Neural networks are already used in a wide range of applications of adaptive non-linear filters. In the case of most of these applications, the number of input variables of the network is small and the amount of noise on the training signal is relatively low. If these conditions do not prevail, it is frequently difficult to train a network, particularly if rapid adaptation is required.
The transfer characteristic of a general, discrete linear filter can be described by the formula ##EQU1## In this case, g(n) designates the output variable of the linear filter at time n, f(n-i) designates the input variable of the filter at time n-i, and the functions k and r designate the response functions of the discrete linear filter. A so-called FIR filter (filter with a finite pulse response) is provided for the case in which the function r disappears at all times i. The output function of the filter is in this case a linear superposition of instantaneous and preceding input signals and preceding output signals.
This filter structure can be generalized to form a non-linear filter architecture, which is given by the formula EQU g(n)=N[f(n), . . . , f(n-M); g(n-1), . . . , g(n-K)] (2)
In this case, the output function N depends in a non-linear manner on the input and output signals. The non-linear function N is in this case approximated by a neural network, which is the case for the filter architecture proposed by Lapedes and Farber (A. Lapedes, R. Farber, "How neural nets work." In Neural information processing systems, ed. D. Z. Anderson, pages 442-456, New York, American Institute of Physics, 1988) Waibel (A. Waibel, "Modular construction of time-delay neural networks for speech recognition", Neural Computation, Vol. 1, pages 39-46, 1989) has described a neural network in the case of which only the input signals of preceding times are supplied to the input variables.